Brms correlation between two ordinal variebles

General
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1

Understanding correlation between 2 ordinal variables Relevance_to_outgroup ~ Relevance_to_ingroup in 2 X 2 design (2 groups and 2 within variables? Is this the correct technique

option one a model for each group + control the within var (Theme):

bf_ingroup <- brms::bf(Relevance_to_ingroup ~ Theme  + (1|p|p_id) ) + cumulative("logit")
bf_outgroup <- brms::bf(Relevance_to_outgroup ~ Theme  + (1|p|p_id) ) + cumulative("logit")

fit_minority <- brm(
  bf_ingroup + bf_outgroup + set_rescor(FALSE),
  data = filter(Control, Group == "Minority"), chains = 4, cores = 24, warmup = 2000, iter = 4000,  seed=123)

The results suggest high correlation:
Multilevel Hyperparameters:
~p_id (Number of levels: 29)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Relevancetoingroup_Intercept) 2.15 0.29 1.66 2.80 1.00 1122 2278
sd(Relevancetooutgroup_Intercept) 2.13 0.29 1.65 2.77 1.00 1128 2305
cor(Relevancetoingroup_Intercept,Relevancetooutgroup_Intercept) 1.00 0.00 0.99 1.00 1.00 6137 5361

but can I argue that the Theme does not effect the correlation since:
Relevancetoingroup_ThemeNeutral -1.02 0.10 -1.21 -0.84 1.00 10428 6160
Relevancetooutgroup_ThemeNeutral -0.87 0.09 -1.06 -0.69 1.00 10607 5816
Or am I looking on this data totally wrong.

2

Yes, the model suggests a very strong correlation between the random intercepts for Relevance_to_outgroup and Relevance_to_ingroup. It’s hard to answer whether this is the correct technique, though. Were you looking to focus on the correlations among the random intercepts, or were you looking for something more like an ordinal version of a Pearson’s correlation? If the former, you’re in good shape. With the later, no, this is not the same thing.

3

Hi Thank you for your response. This is a small (but significant) component of a larger project that I am analyzing using Bayesian ordinal regression by brms.
In this section of the study, I have two independent groups of participants (between factors), and each participant in each group rates two stimuli on an ordinal scale with two DV (within factors). I already know from the descriptive plot of raw data that these two DV are strongly correlated in all levels of my IV. The best statistical method for me was to evaluate everything together, however brms does not yet allow this option for non-normal models (such as ordinal). So my issue is, if this is the present limitation of brms, what are my options, given that the entire project is based on Bayesian foundations, and I would prefer to continue down this path.

4

I’m not so sure this is a limitation of brms. Rather, I think you need to be careful about how you might extend the simple notion of a Pearson’s correlation to a context it wasn’t really designed for, or even wether it’s even worth your effort to do so.

5

But, if I set aside the Bayesian perspective and ask myself if there is a correlation between two ordinal measurements, I will most likely apply the Spearman test. My question is, what are the Bayesian alternatives? and whether brms is the appropriate tool.

6

I’m not really up on nonparametric statistics, so others will have to chime in on analogues to a Spearman test. Even from a frequentist perspective, though, I’d wonder about whether Spearman test would be appropriate here. Would such a test not ignore the experimental structure, and therefore return dubious results?